It is instructive to compare the absorption band structures for a single particle and their ensemble.
For a single particle the absorption band has the Lorentzian shape, while due to non-homogenous broadening (occurring as a result of the ensemble averaging) it acquires the Gaussian shape. If the values \({\bar{\gamma }_n}\)  and \({\bar{\delta }_n}\)  are comparable the fine structure components have a rather complicated shape consisting of the Gaussian central part and Lorentzian tails.
Let us stress that in the ensemble of nano-particles decay of the reservoir states (due to vibron-phonon interactions) suppresses the Loschmidt echo signal. Indeed as we said already above, to study the initially prepared state evolution in the ensemble of nano-particles, one has to average the initial state amplitude over the random distribution of the phonon configurations. This procedure leads to the broadening of the Loschmidt echo components. Then the number of observable recurrence cycles decreases. Only a finite number of the reservoir states is essential for the time evolution of the initial state, and this number is on the order of the \(S R\)  interaction region width, \(\Gamma \) . In fact for the Zwanzig model with finite number of the reservoir states the time evolution is almost the same as that for the infinite reservoir systems
[1]}.
